Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
[41.] COMMENTARIVS.
[42.] LEMMA I.
[43.] LEMMA II.
[44.] LEMMA III.
[45.] LEMMA IIII.
[46.] LEMMA V.
[47.] LEMMA VI.
[48.] II.
[49.] III.
[50.] IIII.
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page |< < of 213 > >|
126FED. COMMANDINI
Itaque quoniam duæ lineæ K l, l m ſe ſe tangentes, duabus
lineis
ſe ſe tangentibus a b, b c æquidiſtant;
nec ſunt in eo-
dem
plano:
angulus K l m æqualis eſt angulo a b c: & ita an
1110. unde
cimi
gulus l m K, angulo b c a, &
m K lipſi c a b æqualis prob abi
tur
.
triangulum ergo K l m eſt æquale, & ſimile triang ulo
a
b c.
quare & triangulo d e f. Ducatur linea c g o, & per ip
ſam
, &
per c f ducatur planum ſecans priſma, cuius & paral
lelogrammi
a e communis ſectio ſit o p q.
tranſibit linea
f
q per h, &
m p per n. nam cum plana æquidiſtantia ſecen
tur
à plano c q, communes eorum ſectiones c g o, m p, f q
ſibi
ipſis æquidiſtabunt.
Sed & æquidiſtant a b, K l, d e. an-
guli
ergo a o c, K p m, d q f inter ſe æquales ſunt:
& ſunt
2210. unde-
cimi
æquales qui ad puncta a k d conſtituuntur.
quare & reliqui
reliquis
æquales;
& triangula a c o, _K_ m p, d f q inter ſe ſimi
lia
erunt.
Vtigitur ca ad a o, ita fd ad d q: & permutando
334. ſexti ut c a ad fd, ita a o ad d q.
eſt autem c a æqualis fd. ergo &
a
o ipſi d q.
eadem quoque ratione & a o ipſi _K_ p æqualis
demonſtrabitur
.
Itaque ſi triangula, a b c, d e f æqualia &
ſimilia
inter ſe aptétur,
83[Figure 83] cadet linea f q in lineam
c
g o.
Sed & centrũ gra
44per 5. pe-
titionem

Archime

dis
.
uitatis h in g centrũ ca-
det
.
trãſibit igitur linea
f
q per h:
& planum per
c
o &
c f ductũ per axẽ
g
h ducetur:
idcircoq; li
neam
m p etiã per n trã
ſire
neceſſe erit.
Quo-
niam
ergo ſh, c g æqua-
les
ſunt, &
æquidiſtãtes:
itemq; h q, g o; rectæ li-
neæ
, quæ ipſas cónectũt
c
m f, g n h, o p q æqua-
les
&
æquidiſtãtes erũt.

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